
theorem
  for C1, C2 being Coherence_Space ex f being U-stable Function of C1,
  C2 st Trace f = {}
proof
  let C1, C2 be Coherence_Space;
  reconsider X = {} as Subset of [:C1, union C2:] by XBOOLE_1:2;
A1: for a,b being Element of C1 st a \/ b in C1
 for y being object st [a,y] in
  X & [b,y] in X holds a = b;
  ( for x being set st x in X holds x`1 is finite)& for a,b being Element
of C1 st a \/ b in C1
 for y1,y2 being object st [a, y1] in X & [b,y2] in X holds {
  y1,y2} in C2;
  hence thesis by A1,Th38;
end;
